On representation varieties of 3–manifold groups

Kapovich, Michael¹ ; Millson, John²

¹ Department of Mathematics, University of California, Davis, 1 Shields Ave, Davis, CA 95616, United States, Korea Institute for Advanced Study, 207-43 Cheongnyangri-dong, Dongdaemun-gu, Seoul, South Korea
² Department of Mathematics, University of Maryland, College Park, College Park, MD 20742, United States

Geometry & topology, Tome 21 (2017) no. 4, pp. 1931-1968.

Résumé

We prove universality theorems (“Murphy’s laws”) for representation varieties of fundamental groups of closed $3$–dimensional manifolds. We show that germs of $SL\left(2\right)$–representation schemes of such groups are essentially the same as germs of schemes over $\mathbb{Q}$ of finite type.

Détail

DOI : 10.2140/gt.2017.21.1931

Classification : 14B12, 20F29, 57M05
Keywords: character varieties, $3$–manifold groups

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